a.) A doctor wants to estimate the HDL cholesterol of all 20-to 29-year-old fema
ID: 3046062 • Letter: A
Question
a.)
A doctor wants to estimate the HDL cholesterol of all 20-to 29-year-old females. How many subjects are needed to estimate the HDL cholesterol within 3 points with 99% confidence assuming = 14.9? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required? A 99% confidence level requires subjects. (Round up to the nearest whole number as needed.) A 95% confidence level requires | | subjects Round up to the nearest whole number as needed.) How does the decrease in confidence affect the sample size required? A. B. O C. The lower the confidence level the smaller the sample size. The lower the confidence level the larger the sample size The sample size is the same for all levels of confidence.Explanation / Answer
Solution:-
a) E = 3, = 14.9, Z0.005 = 2.58 , Z0.025 = 1.96
=> A 99% confidence level requires 164 subjects.
-> n = [ (Z /2 × ) ÷ E ] 2
= ((2.58*14.9)/3)^2
= 164.19859
= 164
=> A 95% confidence level requires 95 subjects.
-> n = [ (Z /2 × ) ÷ E ] 2
= ((1.96*14.9)/3)^2
= 94.7637
= 95
=> option A. The lower the confidence level the smaller the sample size.
b) Given that Z0.05 = 1.645 , E = 0.04
=> "no preliminary estimate is available" so assume that p = 0.5
n = p(1-p)(z/E)^2
n = (0.5)(1-0.5)(1.645/0.04)^2
n = 422.8164
n = 423
=> Now we are told that p = 0.42
n = 0.42*(1-0.42)(1.645/0.04)^2
n = 411.992
n = 412
=> option B. Having an estimate of the population proportion reduces the minimum sample size needed.
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